Question

Mark Price, the new productions manager for Speakers and Company, needs to find out which variable most affects the demand for their line of stereo speakers. He is uncertain whether the unit price of the product or the effects of increased marketing are the main drivers in sales and wants to use regression analysis to figure out which factor drives more demand for its particular market. Pertinent information was collected by an extensive marketing project that lasted over the past 12 years and was reduced to the data that follow:

YEAR	UNIT SALES (THOUSANDS)	PRICE $/UNIT	ADVERTISING ($000)
1	388	289	580
2	688	217	826
3	888	209	1,114
4	1,310	215	1,410
5	1,153	217	1,212
6	1,189	206	1,310
7	888	215	904
8	1,114	203	1,114
9	983	217	705
10	1,331	209	904
11	923	222	705
12	817	239	685

a. Perform a regression analysis based on these data using Excel. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

y¯y¯ =  +  Price +  Advertising

c. Predict average yearly speaker sales for Speakers and Company based on the regression results if the price was $288 per unit and the amount spent on advertising (in thousands) was $888. (Enter your answer in thousands. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Forecasted sales             thousand units

Answer 1

a. sales = y (dependent variable)

price and advertising are the two independent variables.

Form of this equation: y (sales) = b1+b2*price+b3*advertising

In excel, enter data in the following format:

The next step in excel is to go to "data", select "data analysis" and then select "regression". The input y range should be the values of sales from 1998 to 2009 and then input x range should select values of price and advertising.

Thus, b1 = 2058.3448 (intercept) , b2 = -6.4766 (x variable 1) and b3 = 0.3736 (x variable 2)

Thus y = 2058.3448 - 6.4766 * price + 0.3736 * advertising.

c. Now substituting the values of price = 287 and advertsing = 887 in the regression equation:

y = 2058.3448 - 6.4766*287 + 0.3736*887

= 2058.3448 - 1858.7888+331.3947

= 530.95 or 531 (rounded off to the nearest whole number).